The Picard group of topological modular forms via descent theory
نویسندگان
چکیده
منابع مشابه
Elliptic points of the Picard modular group
We explicitly compute the elliptic points and isotropy groups for the action of the Picard modular group over the Gaussian integers on 2-dimensional complex hyperbolic space.
متن کاملAnalysis of a Picard modular group.
Our main goal is to analyze the geometric and spectral properties of the Picard modular group with Gaussian integer entries acting on the two-dimensional complex hyperbolic space.
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The Eisenstein-Picard modular group PU(2, 1;Z[ω]) is defined to be the subgroup of PU(2, 1) whose entries lie in the ring Z[ω], where ω is a cube root of unity. This group acts isometrically and properly discontinuously on H C , that is, on the unit ball in C2 with the Bergman metric. We construct a fundamental domain for the action of PU(2, 1;Z[ω]) on H2 C , which is a 4-simplex with one ideal...
متن کاملThe geometry of the Gauss-Picard modular group
We give a construction of a fundamental domain for the group PU(2, 1,Z[i]). That is the group of holomorphic isometries of complex hyperbolic space with coefficients in the Gaussian ring of integers Z[i]. We obtain from that construction a presentation of that lattice and relate it, in particular, to lattices constructed by Mostow.
متن کاملExtended Gauss AGM and corresponding Picard modular forms
The latter theorem shows the relation of the (coefficients of the realized) elliptic curves corresponding to two isogenous torus C/Z + τZ and C/Z + 2τZ. So in general this theorem is referred as the isogeny formula for the Jacobi theta constants. Any way these two theorems are telling us a very interesting story concerned with AGM, periods of algebraic varieties, hypergeometric functions and mo...
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ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2016
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2016.20.3133